Hankel Determinant Solutions to Several Discrete Integrable Systems and the Laurent Property
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Publication:5251661
DOI10.1137/130911676zbMath1400.37062arXiv1501.02879OpenAlexW1974970150MaRDI QIDQ5251661
Guoce Xin, Xing-Biao Hu, Xiang-Ke Chang
Publication date: 20 May 2015
Published in: SIAM Journal on Discrete Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1501.02879
Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Special sequences and polynomials (11B83) Continued fraction calculations (number-theoretic aspects) (11Y65) Toeplitz, Cauchy, and related matrices (15B05)
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Cites Work
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- Laurent phenomenon algebras
- Laurent phenomenon sequences
- Discrete integrable systems and Poisson algebras from cluster maps
- A conjecture based on Somos-4 sequence and its extension
- Symplectic maps from cluster algebras
- Discrete integrable systems, positivity, and continued fraction rearrangements
- Non-commutative integrability, paths and quasi-determinants
- Cluster mutation-periodic quivers and associated Laurent sequences
- Generalized Bäcklund-Darboux transformations for Coxeter-Toda flows from a cluster algebra perspective
- The Laurent phenomenon
- Determinantal identities: Gauss, Schur, Cauchy, Sylvester, Kronecker, Jacobi, Binet, Laplace, Muir, and Cayley
- Integrable symplectic maps
- Perfect matchings and the octahedron recurrence
- \(Q\)-system cluster algebras, paths and total positivity
- \(Q\)-systems, heaps, paths and cluster positivity
- The solution of the A\(_{r}\) T-system for arbitrary boundary
- Proof of the Somos-4 Hankel determinants conjecture
- Binomial determinants, paths, and hook length formulae
- Bäcklund transformations and their applications
- T-systems with boundaries from network solutions
- Positivity of the \(T\)-system cluster algebra
- Singularity confinement for maps with the Laurent property
- Laurent polynomials and superintegrable maps
- Hankel determinants for some common lattice paths
- The generating function of ternary trees and continued fractions
- Advanced determinant calculus: a complement
- Cluster algebras I: Foundations
- Mutation-periodic quivers, integrable maps and associated Poisson algebras
- Cluster algebras IV: Coefficients
- Integrality and the Laurent phenomenon for Somos 4 and Somos 5 sequences
- Integrable maps
- ELLIPTIC CURVES AND QUADRATIC RECURRENCE SEQUENCES
- Diophantine non-integrability of a third-order recurrence with the Laurent property
- Sigma function solution of the initial value problem for Somos 5 sequences
- A family of linearizable recurrences with the Laurent property
- Total positivity: tests and parametrizations.
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